Constraining the Far-Field in Situ Stress State Near a Deep South African

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Constraining the far-ﬁeld in situ stress state near a deep South African gold mine

Amie M. Lucier a,b,Ã, Mark D. Zoback b, Vincent Heesakkers c, Ze’ev Reches c, Shaun K. Murphy d a Shell International Exploration and Production, PO Box 481, Houston, Texas 77001-0481, USA b Stanford University, Stanford, California c University of Oklahoma, Norman, Oklahoma d AngloGold Ashanti, South Africa article info abstract

Article history: We present and test a new technique for determining the far-field virgin state of stress near the TauTona Received 24 March 2008 gold mine. The technique we used to constrain the far-field stress state follows an iterative forward Received in revised form modelling approach that combines observations of drilling-induced borehole failures in borehole 31 July 2008 images, boundary element modelling of the mining-induced stress perturbations, and forward Accepted 12 September 2008 modelling of borehole failures based on the results of the boundary element modelling. Using this approach, we constrained a range of principal stress orientations and magnitudes that are consistent Keywords: with all the observed failures and other stress indicators. We found that the state of stress is a normal In situ stress faulting regime ðSv oSHmax oShmin Þ with principal stress orientations that are slightly deviated from Mines vertical and horizontal and, therefore, denoted with a (*). The maximum principal stress, S , is deviated Breakouts v 101 from vertical plunging towards the NNW with a magnitude gradient of 27 MPa/km. The Drilling-induced tensile fractures 1 Boundary element modelling intermediate principal stress, SHmax , is inclined 10 from horizontal plunging towards an azimuth of Induced micro-seismicity 1561 and has a magnitude gradient of 24 MPa/km. The least principal stress, Shmin , is inclined 51 from horizontal plunging towards an azimuth of 2471 and has a magnitude gradient of 14 MPa/km. This stress state indicates that the crust is in a state of frictional faulting equilibrium, such that normal faulting is likely to occur on cohesionless pre-existing fault planes that are optimally oriented to the stress field. Modelling of breakout rotations and gaps in breakout occurrence associated with recent fault slip on critically stressed faults located 4100 m from the mine further confirmed this stress state. & 2008 Elsevier Ltd. All rights reserved.

1. Introduction the far-field stress will lead to better modelling of the mining- induced stress perturbations around the excavation. In turn, this As mining around the world moves deeper underground, can guide mining activities in the future and improve overall understanding the stress field at depth, and how mining activity safety in the mines. perturbs it, becomes increasingly important for mine safety. As a Constraining the far-field stress state is an important part of result of the mining-induced stress perturbations, deep under- the Natural Earthquake Laboratory in South African Mines ground mines tend to have appreciable mining-induced seismicity (NELSAM) project, which is working to develop a near-field associated with them. Near the gold mines in the Witwatersrand laboratory to study earthquakes at seismogenic depths [4–6]. The Basin of South Africa, some of the deepest mines in the world, deep gold mines of South Africa are unique locations for near-field seismicity was first reported in 1908, about twenty years after the studies of earthquake mechanics because of the high rate of onset of gold mining in the region. Gane et al. [1] first directly mining-induced seismicity and the direct access to faults at associated the seismicity with the mining. Later, Gane et al. [2] seismogenic depths. However, the perturbation of the in situ established the close proximity of the event locations to the active stresses by the large-scale mining activities creates a complex mining faces. McGarr et al. [3] showed that most of the seismicity stress field that complicates our understanding of the physical occurs in regions near the mining face with very large mining- mechanisms controlling the induced seismicity. As part of the induced stress perturbations. A more complete characterisation of NELSAM project, we developed a new method to constrain the far- field in situ stress state surrounding the TauTona gold mine in the Western Deep Levels of the Witwatersrand Basin of South Africa. Ã Corresponding author at: Shell International Exploration and Production, PO Box 481, Houston, TX77001-0481, USA. Tel.: +1650 269 4597. Much of the previously published work on characterizing the E-mail address: [email protected] (A.M. Lucier). far-field in situ stress state near the deep mines in the

Please cite this article as: Lucier AM, et al. Constraining the far-ﬁeld in situ stress state near a deep South African gold.... Int J Rock Mech Mining Sci (2008), doi:10.1016/j.ijrmms.2008.09.005 ARTICLE IN PRESS

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Witwatersrand Basin relies on borehole strain relief measure- stress indicators observed in the near- and far-ﬁeld to the mining ments [7–9]. In their review of global stress measurements, excavation. McGarr and Gay [10] showed that in South Africa the stress state at depths below 2 km is typically a normal faulting stress regime, in which the vertical stress exceeds the horizontal stresses. These 2. Data measurements also show that the minimum horizontal stress,

Shmin, magnitude is typically much lower than the vertical stress 2.1. Mine layout and rock properties magnitude, Sv, although there was considerable scatter in the measurements. Because the mine excavations perturb the in situ stress state, a In this study, we use both near- and far-field observations of clear understanding of the geometry of the mine layout and the stress indicators and boundary element modelling to constrain material properties of the in situ rock and backfill is critical. The the far-field stress state and model the near-field perturbation of geometry of the mine is illustrated in Fig. 1. The mining occurs that stress state. The stress indicators used in the analysis are along 0.5–1.5 m thick planar deposits of gold-bearing conglomer- drilling-induced failures (i.e., breakouts and drilling-induced ates, referred to as ‘‘reefs’’. In the TauTona mine, the Carbon Leader tensile fractures (DITFs)) observed in image logs from boreholes Reef is mined; in the shallower Mponeng mine (red), which drilled within the mine at a variety of orientations. Peska and overlaps TauTona towards the southwest, the Ventersdorp Contact Zoback [11] discussed the mechanics controlling the formation of Reef is mined. The bedding dips about 201 towards the SSE. compressive and tensile failures in boreholes drilled at arbitrary The NELSAM study area is located in the tunnels below the orientations to principal stresses. These features have previously stope in the southeastern part of the mine. The reef in this region been used to constrain the stress states around oil and gas fields is offset by the Pretorius Fault Zone (PFZ), an ancient normal to and other deep boreholes [e.g., 12]. Stacey and Wesseloo [13] strike-slip fault zone that dips steeply and strikes approximately review the use of these features for evaluating in situ stresses in NE-SW. This is an area of active mining and is near the deepest deep mines. Because of the complexity of the stress perturbation part of the mine at a depth of approximately 3.6 km. In Fig. 1d, around the mining excavation, the addition of boundary element the active mining region is categorized into three mining steps modelling was necessary to analyse the drilling-induced failures (1, 2, and 3) that represent the extent of mining at June 2005, observed in the near-field of the excavation. The technique we January 2006, and June 2006, respectively. These correspond to present follows an iterative forward modelling approach to the times at which borehole drilling and image logging occurred. constrain the far-field stress state that is consistent with the The access tunnels have a more localised effect (out to 2 tunnel

Plan View of TauTona and Mponeng Perspective View of TauTona and Mponeng from East to West Depth: 2350m N 012 N km Down 800 m

Depth: 3650 m Shaft NELSAM Pillar Perspective View of NELSAM Study Area from East to West Pretorius Fault Zone N Stope 118 level tunnels NELSAM Down

50m

120 level tunnels

Map View of Active Mining Steps in NELSAM Study Area

N 118 level tunnels Pretorius Fault Intact host rock (pillars) Zone Old mining region: No Backfill Mponeng mine: Backfill TauTona mine: Backfill Mining Step 1 120 level tunnels 1 2 3 Active mining, opposite side of Pretorius Mining Step 2 Fault: Backfill Mining Step 3

Fig. 1. Layout of the mine. (A) Plan view of the stope of Mponeng mine (red) and TauTona mine (blue, green, and yellow) and the PFZ (black). The white area represents the intact host rock and the colour regions indicate the area that has been mined. The NELSAM study area is in the southeastern part of TauTona. (B) Perspective view of the stope from the east without the PFZ. The NELSAM study area is located in the deepest part of the mine. Mponeng is about 800 m shallower than TauTona. (C) Zoomed in perspective view of the NELSAM study area from the east. The active mining (yellow) is offset from the older mining (green) by displacement along the PFZ. The 118 and 120 level tunnels are also shown; they are separated by 50–60 m. (D) Map view of the NELSAM study area tunnels, the PFZ, and the active mining section, which is broken into three mining steps. The older mining region (green) of the stope is not shown so that the tunnels are visible.

A.M. Lucier et al. / International Journal of Rock Mechanics & Mining Sciences ] (]]]]) ]]]–]]] 3 radii) on the stress state than the stope. Therefore, for the purpose displacements and the shear and normal stresses acting on the of this work, they are only modelled in the NELSAM area where material. borehole logging was carried out as shown in Figs. 1c and d and 2. The intact host rock is primarily quartzite. The average material properties for the host rock used in the modelling 2.2. Borehole camera image logs include a uniaxial compressive strength of 200 MPa, Poisson’s ratio of 0.20 and a Young’s modulus of 70 GPa, as based on Borehole image logs provide oriented images of the walls of the laboratory measurements [14,15]. These values have been used in boreholes. Drilling-induced borehole failures such as DITFs and previous studies in TauTona [16].InFig. 1, the green and yellow borehole breakouts as well as natural fractures that intersect the regions represent backfilled excavations in TauTona and the red boreholes can be observed in these image logs. In this work, image represents the backfilled excavation in Mponeng. The backfill is a logs were collected in six 6.6–11.5 m vertical boreholes (sites 2 slurry of waste material that is pumped back into the excavation and 3 in the 118 level and sites 7 V, 9, 10, and 13 in the 120 level), to provide support. The material properties of the backfill in five 9.6–39-m long boreholes deviated 43–801 from vertical TauTona and Mponeng were provided by the mine engineers and (3 boreholes at site DAF in the 118 level and site 7 N and 7 S in are calibrated based on previous modelling by the mining the 120 level), and in the long subhorizontal LIC118 borehole in engineers (Shaun Murphy, personal communication). The backfill the 118 level (Fig. 2). The LIC118 borehole is deviated 70–851 from materials have no cohesion or tensile strength and a friction angle vertical towards the east and 418 m of image log data were of 101. The Mponeng backfill has a shear modulus of 10 MPa and a collected. Logging at sites 10, 13, and LIC118 corresponds to normal modulus of 16 MPa and TauTona backfill has a shear mining step one (June 2005), logging at sites 9 and DAF 1 modulus of 14.4 MPa and a normal modulus of 14.4 MPa. The corresponds to mining step two (January 2006), and logging at shear and normal moduli relate the elastic shear and normal sites 2, 3, 7, and DAF 5 and DAF BIO corresponds to mining step

Plan View of NELSAM Study Area Tunnels and Borehole Locations N

LIC118 (subhorizontal borehole)

418 m logged with camera 2 3 1

BIO DAF 118 level 13 5 tunnels 10 9

N V 7 S 0 100 200 120 level tunnels m

Fig. 2. Locations of boreholes logged in the 118 and 120 level tunnel systems. Sites 2, 3, 7V, 9, 10, and 13 are vertical boreholes. The three boreholes at the DAF site (1, 5, and BIO) and two boreholes at site 7 (N, S) are deviated. The LIC118 borehole is sub-horizontal and extends away from the mining into the far-ﬁeld.

Site 10 Site 13 NWES N NWES N

Poorly Formed Breakouts 6.5 2.0

2.5 7 Breakouts

Tensile Borehole Length (m) Fractures 7.5 3.0

Fig. 3. Example borehole image logs from sites 10 and 13. Images are shown in an unwrapped borehole view and are oriented with north on the sides of the images and south in the centre of the images. The site 10 image illustrates DITFs and poorly formed breakouts, while site 13 shows breakouts.

4 A.M. Lucier et al. / International Journal of Rock Mechanics & Mining Sciences ] (]]]]) ]]]–]]] three (June 2006). Fig. 3 shows examples of drilling-induced although the breakouts were poorly formed. Site 13 and LIC118 failures observed in the image logs. boreholes both had breakouts. Two of the boreholes at the DAF site (5 and BIO) and the vertical borehole at site 7 (V) had DITFs. In 2.3. Overcoring measurements some of the boreholes, no drilling-induced failures were observed. The image log collected in borehole 1 at the DAF site was of poor In February 2000, two in situ stress measurements were quality and could not be analysed. completed within the shaft pillar using the overcoring technique The LIC118 borehole was of particular importance for this and reported in an internal report [14]. These tests were carried analysis, because it was drilled into the far-field stress state away out in the roof of a tunnel in the shaft pillar area at the 83 level from the mining excavation. Breakouts occurred starting at a (2361 m deep). The measurements were about 10.5 m into the measured depth of 35 m and were observed throughout the length of the borehole (Fig. 5). A large-scale rotation in the position of the access boreholes. The maximum principal stress (S1) was deviated about 201 from vertical plunging towards the NNW. The magni- breakouts around the borehole walls occurred between 35 and about 150 m measured depth. From 150 m to the end of the tude gradient of S1 was about 36 MPa/km which is significantly higher than the predicted vertical stress gradient of 27 MPa/km borehole, the breakout positions and widths were relatively based on an average overburden density of 2700 kg/m3. This is consistent, confirming that the borehole is extending into the likely due to the stress concentration in the shaft pillar which is far-field stress state. The breakouts formed on the sides of the supporting the excess vertical load resulting from the excavation of borehole suggesting a vertically oriented maximum compression. Localised rotations in the breakout position as well as gaps in the stope. The intermediate principal stress (S2) was deviated about 201 down from the horizontal towards the SSE and had a breakout occurrence were also observed throughout the length of magnitude gradient of about 19 MPa/km. The minimum principal the borehole image log. stress (S3) was nearly horizontal in the WSW direction with a gradient of about 10 MPa/km. Therefore, the nearly horizontal principal stress components in the shaft pillar region are 3.2. Building boundary element model significantly anisotropic. These measurements are generally consistent with the normal faulting stress state for South Africa A boundary element modelling program Map3D [17], which reported by McGarr and Gay [10]. was developed for mining applications, was used to numerically model the response of the rock to the mining activity. Map3D is based on an indirect boundary element method. The program has 3. Methodology for constraining the far-field stresses been used to examine the stress perturbation from mining and the associated failure in several mine settings [e.g., 18–20]. The We followed an iterative forward modelling approach to model accounts for the geometry of the stope and access tunnels, characterize the far-field in situ stress state near TauTona mine the structural support provided by backfill materials, and the (Fig. 4). Each step of the workflow is described in the following stress loading conditions applied by the far-field in situ stress sections. The final result was to constrain the range of principal state. The model simulates the rock mass response to these stress orientations and magnitudes that are consistent with all the inputs while honouring the physical constraints of equilibrium, observed data. continuity, and elasticity. The model space begins as a homo- geneous, elastic medium that approximates the in situ host rock; 3.1. Borehole data analysis therefore, far-field boundary conditions are accommodated. The mining excavation and access tunnel are then incorporated as The first step of the workflow is to analyse and document elements and the response to these elements is calculated on the drilling-induced failures observed in the borehole image logs. specified grids. The results of this analysis are summarised in Table 1. Site 10 was The mine geometry shown in Fig. 1 was modelled with two the only borehole where both DITFs and breakouts were observed, types of elements referred to as fictitious forces and displacement discontinuities. Because the access tunnels in the NELSAM study area are void spaces, they were modelled as fictitious force Step 1: Analyze borehole image data for drilling induced failures elements that have zero surface stresses. The stope was modelled with displacement discontinuity elements which had material property values corresponding to the appropriate backfill materials modelled with an elasto–plastic constitutive law. Step 2: Build Boundary Element Model (BEM) that representssents The stress state at each borehole needed to be analysed based mining geometry and material properties on the extent of the mining at the time of the camera logging. This corresponds to three mining steps: June 2005, January 2006, and June 2006 (Fig. 1d). The BEM simulates the stress perturbations Step 3: Constrain initial far-field stress state after each of these mining steps and calculates the results on specified grids (at the borehole locations, on planes of interest near the boreholes, and along mapped fault planes) within the model. Step 4: Model borehole failures with results of BEM at borehole locations 3.3. Initial far-field stress model estimate

The goal of the workflow is to constrain the far-field stress Step 5: Compare modelled failures with all observed failures state that is consistent with the observed stress indicators. To do • Poor Fit: Repeat steps 3-5 with updated stress model this, we first estimate a far-field stress model to be used as the • Good Fit: Constrain range of stress models initial condition to solve for the mining-induced stress perturba- Fig. 4. Iterative forward modelling workflow for constraining in situ far-field tions with the BEM. This model defines the principal stress stresses. orientations and magnitudes and pore pressure, and it provides a

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Table 1 Borehole observations of breakouts and DITFs

Borehole Tunnel level Borehole trajectory Length (m) Drilling-induced failure observations Image quality

Site 2 118 Vertical 7.1 No failures observed Good Site 3 118 Vertical 8.5 No failures observed Good Site 7N 120 Dev: 471 10.5 No failures observed Fair Azi: 1421 Site 7V 120 Vertical 9.4 DITF: Good 6 m: position 2221, inclination 101 8 m: position 1981, inclination 11 9 m: position 1701, inclination 1791 Site 7S 120 Dev: 431 9.6 Low-quality data, no clear evidence for failures Poor Azi: 3221 Site 9 120 Vertical 11.4 No failures observed Good Site 10 120 Vertical 11.5 DITF: Good 6 m: position 161 1, inclination 121 9 m: position 152 1, inclination 160 1 Breakouts: Poorly formed, position 621,width 201 Site 13 120 Vertical 6.6 Breakouts: Good Well formed, some localized rotation Position 55–651,width 401 DAF 2 118 Dev: 1101 (201 up from horizontal) 39 Low-quality data Poor Azi: 3461 DAF 5 118 Dev: 701 19 DITF: Good Azi: 1561 5 m: position 901, inclination 151 15 m: position 1051, inclination 1761 DAF BIO 118 Dev: 1101 (201 up from horizontal) 37.9 Low-quality data Poor–fair Azi: 3531 DITF Evidence from 5 to 10 m: Position: 145–1701, Inclination 301 LIC118 118 Dev: 75–851 418 (logged) Breakouts along extent of borehole, see Figs. 4–6 Fair–good Azi: 901

For borehole trajectory, Dev is deviation from vertical and Azi is borehole azimuth.

starting point for the iterative forward modelling used to area directly around the mine makes Pp difficult to quantify. constrain the stress model. Within the mine, Pp is considered to be negligible. However, given the low permeability of the rocks in TauTona (1020 m2), the 3.3.1. Stress regime diffusion rates are on the order of 30 m over 10 years or 70 m over We initially assumed that the principal stresses were oriented 50 years [22]. Based on these rates, we estimated that the influence of the dewatering extends about 100 m away from the vertically (Sv) and horizontally (SHmax and Shmin). While this is a simple assumption, it is often observed in stable cratonic crust mine. Previous studies have shown that hydrostatic Pp is observed [21] around the world. We also assumed a normal faulting stress around the world in deep boreholes, even those in low porosity ( 2%) and very-low permeability crystalline rocks [22–24]. regime such that SvXSHmaxXShmin. This was based on the o observations of McGarr and Gay [10], the overcoring measure- Therefore, it was assumed that the far-field virgin stress state ments, and the position of the breakouts observed in the LIC118 has hydrostatic despite the dewatering and general dryness borehole. observed in the mine.

3.3.5. S magnitude 3.3.2. Horizontal stress orientations hmin Breakout rotations and gaps in breakout occurrence were We used information from the overcoring stress measurements observed throughout the length of the LIC118 borehole image log. and the drilling-induced failures observed in the vertical bore- Previous studies have shown that these features in the observed holes as an initial estimate the orientations of the horizontal breakouts are associated with recent slip on faults [25,26]. This stresses. The overcoring measurements indicated an SHmax suggests that the far-ﬁeld stress state around the mine is likely to azimuth of 1531 [14]. The DITFs at site 10 suggest an SHmax be critically stressed (i.e., faults which are well-oriented to the azimuth of 1581 and the breakouts observed at site 13 borehole stress ﬁeld are near the point of frictional slip). Thus, frictional suggest an SHmax azimuth of 1551. Based on these three consistent faulting theory could be used to constrain the maximum observations, we chose an initial SHmax orientation of 1551 and an difference between the vertical principal stress magnitude (S1 in orthogonal Shmin azimuth of 2451. normal faulting areas) and the minimum principal stress

magnitude, S3 [12]. In frictional faulting theory, the ratio of the 3.3.3. Vertical stress magnitude maximum effective stress (s1) to the minimum effective stress The initial Sv magnitude results from the weight of the (s3) is controlled by the coefficient of friction (m) of optimally overburden material. The average density of the overburden at 3 oriented faults in the crust. TauTona was estimated to be 2700 kg/m . By integrating the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S P s density over the depth of the mine, the average Sv gradient was 1 p ¼ 1 ¼ð m2 þ 1 þ mÞ2 (1) estimated to be 27 MPa/km. S3 Pp s3

This equation deﬁnes the upper limit for the s1/s3 ratio. The 3.3.4. Pore pressure general range for m observed in the brittle upper crust is 0.6–1.0

No direct measurements of the pore pressure, Pp, have been [27,28]. Solving for S3 in Eq. (1) using m ¼ 1 predicts the lower made in or around the mine. Furthermore, the dewatering of the bound for S3 to be 13 MPa/km (S1 ¼ 27 MPa/km, Pp ¼ 10 MPa/km).

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LIC118 Breakout Observations 3.4. Modelling borehole failure with BEM results Bottom Top Bottom Drilling-induced borehole failures result from the concentration of the effective stresses around the borehole walls during and after drilling. The position and width of the drilling-induced failures (and angle of inclination for the case of en echelon DITFs) 50 depends on the relative orientations of the borehole and the principal stresses [11]. Breakouts form when the stress concentration at the borehole wall exceeds the rock strength. DITFs form when the tensile stress concentration at the wellbore wall is less than the tensile strength of the rock. In a vertical borehole with 100 principal stresses oriented vertically and horizontally, breakouts

form in the direction of Shmin and DITFs form in the SHmax direction. However, when the borehole and/or the principal stress orientations are deviated from vertical, there is no simple relationship between the stress orientations and the position 150 around the borehole at which the drilling-induced failures will occur [11]. In this study, we used a forward modelling tensor transforma- tion technique to model failures, because for all the cases the boreholes and/or stress ﬁeld were deviated from vertical. The 200 mining-perturbed principal stress magnitudes and orientations at locations along the boreholes were solved for using the BEM. The

Measured Depth, m far-ﬁeld stress model from step 3 provided the initial conditions for the model. Using the (1) mining-perturbed stresses at the borehole locations, (2) borehole orientations, and (3) rock 250 properties, the expected borehole failures were predicted. The results of both the BEM calculation using the initial far-ﬁeld stress model and the breakout modelling based on those results are shown for the LIC118 borehole in Fig. 6. 300 3.5. Comparing borehole failure observations with modelling results

The final step in the methodology is to compare the borehole 350 failures modelled in the previous step to the observed borehole failures in the image logs in all of the boreholes (Table 1). If the modelled failures were not consistent with the observed failures Left Right (based on a qualitative comparison), then the far-field stress model used in the BEM was not considered within the range of Fig. 5. Breakout observations in the LIC118 borehole. These are shown as an acceptable models. The results from the LIC118 borehole had the ‘‘unwrapped’’ borehole wall, with angle around the hole plotted with measured most weight, because these were less dependent on the details of depth. Breakout positions are plotted in a borehole reference frame that is relative the boundary element model and they sample the far-field stress to the bottom of the borehole looking down the borehole. The widths of the breakouts are also indicated. state. Overall, the modelled breakouts for LIC118 using the initial far-field stress model were consistent with the observed breakouts, although the modelling did not predict the absence of breakouts at the beginning of the borehole (Fig. 6b). In the other boreholes, the modelled failures using the initial

3.3.6. SHmax magnitude model were mostly consistent with the observations. In sites 2, Observations from the overcoring measurements and the DITFs 7N, and 9, where no failures were observed, the modelling observed in the site 10 borehole were used to estimate the predicted no failures. However, at sites 3 and 7S, where no failures magnitude of the intermediate stress, SHmax. The minimum and were observed, the modelling predicted the formation of DITFs at maximum horizontal stress magnitudes measured from over- the beginning of the boreholes. Breakouts and DITFs were coring differ by nearly a factor of two. Likewise, the presence modelled at site 10 in the observed orientations, but the breakouts of DITFs at site 10 suggested significant horizontal stress at both sites 10 and 13 were modelled with larger than the anisotropy [12]. Therefore, the initial SHmax gradient was esti- observed widths. At site 7 V, the modelled DITFs were consistent mated to be 26 MPa/km, which is twice that of Shmin but slightly with the observations. However, breakouts were modelled less than Sv. although they were not observed in the borehole. In both the In summary, the initial far-field stress state model was a BIO and the boreholes at the DAF site, DITFs were modelled and normal faulting regime with Sv, SHmax, Shmin, and Pp gradients observed. of 27, 26, 13, and 10 MPa/km, respectively. The SHmax azimuth The initial stress model provided a good starting point for the is 1551 and the Shmin azimuth is 2451. While these stress analysis. To determine the range of stress models consistent with magnitudes and orientations provided a reasonable starting point the observations, steps 3–5 in the methodology (Fig. 4)were for the far-field stress model, as discussed below, each of them repeated by systematically testing each of the assumptions used was subject to revision based on the results of steps 4 and 5 of the to constrain the initial stress state model. Because of the nature of workflow. the borehole image data, the limitations of the boundary element

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Observed (green) and Modeled (blue) Breakouts MPa West East BottomTop Bottom 200 S1 180 160 140 120 100 50 80 60 40 20 0 100

200 S2 180 Stope Intersecti 160 on 150 140 120 100 80 200 60 LIC118 Borehole 40 20 Measured Depth, m 0 250

200 S3 180 160 140 300 120 118 Level 100 80 60 120 Level 40 350 20 0 100 m Left Right

Fig. 6. Boundary element modelling results based on the initial far-ﬁeld stress model. (A) Principal stress orientations (arrows) and magnitudes (colour scale) along a vertical plane extending from the LIC118 borehole trajectory. The intersection of the plane and the stope is shown by a white line. The 118 (red) and 120 (blue) tunnels are shown for reference. (B) Observed (green) and modelled (blue) breakouts along the LIC118 borehole. The data is plotted in a borehole reference frame looking down hole.

modelling, and the forward modelling approach, the solution to 4.1. Far-field stress model the far-field stress will be non-unique. The goal of this work was to constrain the range of stress models over which the modelled We constrained the range of far-field stress models that were borehole failures were consistent with the observations. consistent with the observed data in both the near- and far-field of the mining excavation. The far-field stress model is summarised in Fig. 7. The magnitudes of the principal stresses are plotted with 4. Results depth in Fig. 7a and the range of principal stress orientations are shown in the green shaded regions of Fig. 7b. The state of stress is

The initial estimate of the far-ﬁeld stress state was updated by a normal faulting regime ðSv 4SHmax 4Shmin Þ with principal testing the main assumptions used to constrain it. These stress orientations that are slightly deviated from vertical and assumptions were: (1) normal faulting stress regime with vertical horizontal and, therefore, denoted with a (*). The maximum and horizontal principal stresses, (2) horizontal stress orienta- principal stress, Sv , is deviated 0–201 from vertical plunging tions, (3) Sv magnitude, (4) Pp magnitude, (5) Shmin magnitude, towards the NNW and has a magnitude gradient ranging from and (6) SHmax magnitude. The details of these tests are 26.7 to 27.3 MPa/km. The intermediate principal stress, SHmax ,is summarised in Appendix A. This analysis resulted in a well- inclined 0–201 from horizontal plunging towards an azimuth constrained stress model for the region around the TauTona gold between 1451 and 1681 and has a range in magnitude gradient mine which is described below. between 21 and 26 MPa/km. The least principal stress, Shmin ,is The resulting stress model suggests that the crust around inclined 0–101 down from horizontal towards an azimuth TauTona is critically stressed, such that the stress magnitudes are between 2351 and 2581 and has a magnitude gradient ranging constrained by frictional failure equilibrium theory and small from 12.9 to 15.5 MPa/km. A representative far-ﬁeld stress model stress perturbations may lead pre-existing, optimally oriented is shown by the symbols in Fig. 7. The principal stress magnitude faults into failure. We provide further evidence that supports a gradients are 27.2, 24, and 14 MPa/km; and principal stress critically stressed crust by modelling the localised rotations and orientations are an Sv azimuth of 3451 and plunge of 801,an gaps in the occurrence of breakouts observed along the LIC118 SHmax azimuth of 1571 and plunge of 101, and a nearly horizontal image log. We show that these features are associated with faults Shmin with an azimuth of 2471. This stress model was chosen to that are optimally oriented for recent slip. investigate critically stressed faults in the vicinity of the mine.

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Stress Magnitude, MPa 0 50 100 150 Far-Field Stress Orientations 0 North 500

1000 S1

30° 60° 90° 1500

S3 2000 Depth, m 2500 S2

Representative Stress Magnitudes 3000

S1 = Sv* 27.2 MPa/km 3500 NELSAM S2 = SHmax* 24 MPa/km S3 = Shmin* 14 MPa/km Pp Sv* 4000 Pp 10 MPa/km Shmin* SHmax*

Fig. 7. Constrained far-ﬁeld stress model. On the left, the representative principal stress magnitude and Pp gradients (as described on the bottom right) are shown in a pressure versus depth plot. At the depth of the NELSAM study area, the acceptable ranges in stress magnitudes are illustrated with error bars. On the right, a stereonet plot shows the range in acceptable principal stress orientations in the green-shaded regions and the representative stress model orientations with the green symbols.

4.2. Critically stressed crust Likelihood of Slip Based on CFF as a function of fracture pole orientation The far-field state of stress around TauTona is in frictional (lower hemisphere projection) CFF, MPa/km faulting equilibrium as predicted by Mohr-Coulomb failure N criterion, such that the crust is in a constant state of frictional failure along optimally oriented, cohesionless, pre-existing faults 0 (Fig. 8). While the rate of the brittle deformation in shield areas like the Kaapvaal Craton of South Africa is quite slow as compared -2 to most intraplate regions, well-oriented faults are still critically stressed [29]. This frictional failure results in stress drops that -4 limit the stress magnitudes that can be sustained in the crust. A fault plane is optimally oriented, or critically stressed, when the -6 Coulomb failure function (CFF) resolved on the fault is positive. This occurs when the shear stress (t) resolved on the fault plane is -8 greater than the product of the effective normal stress (SnPp, where Sn is normal stress) and m along the fault plane. -10 CFF ¼ t mðSn PpÞ (2) Fig. 8. Lower hemisphere projection stereonet plot of Coulomb failure function Faults dipping 50–851 to the ENE or WSW are critically stressed (CFF) for fracture plane poles in the far-field stress model. Red colours indicate pole in the far-field stress state (Fig. 8). orientations that are critically stressed (positive CFF). Normal faults striking SSE The critically stressed crust near TauTona is supported by and NNW are critically stressed. Analysis assume m ¼ 0.6 and zero cohesion along observations of localised breakout rotations and gaps in breakout the fault surfaces. occurrence along the LIC118 borehole (Fig. 5). Previous work has shown that localised rotations in the position of breakouts and interruptions in breakout formation are associated with stress perturbations from recent slip on nearby faults [25,26].To stressed fault, we predicted the breakout formation expected as a determine if these breakout observations were consistent with result of the orientation of the borehole relative to the stress the constrained stress state, we examined if they could be field, which has been perturbed by both the mining and slip on explained by slip on the natural faults observed in the LIC118 the fault. image logs. First, natural faults corresponding to local breakout We followed the methodology proposed by Barton and Zoback rotations or gaps in the occurrence of breakouts were identified [25] to analyse the breakout rotations and gaps with respect to the in the image log. Then, we determined whether the fault critically stressed faults. First, the local perturbation of the stress orientations were critically stressed (i.e., CFF40) in either the field due to slip on the critically stressed fault was modelled. This virgin (i.e., representative stress state defined above) or mining- required the determination of the slip vector on the fault. The slip perturbed stress state (from BEM calculation). For a critically direction is the direction of maximum shear stress (t) resolved on

A.M. Lucier et al. / International Journal of Rock Mechanics & Mining Sciences ] (]]]]) ]]]–]]] 9 the fault plane, which is a function of the fault orientation and the stress field, mining-perturbed stress field, borehole trajectory, mining-induced stress state at the fault location as described by drilling conditions, and rock properties including rock strength Keilis-Borok [30] for a fault patch of dimensions 2L 2L in Eq. (3). and Young’s. Fig. 9 shows two examples of the breakout modelling analysis 16 2L d ¼ Dt pffiffiffiffi (3) for faults that become critically stressed due to the mining- s 7pG p induced stress changes. Because the faults have become critically The magnitude of the slip vector, d, depends on the fault patch stressed due to the recent mining-induced stress perturbations, it size, the shear modulus of the faulted material, G, and the stress is likely that any slip on these faults occurred recently. In the first drop, Dts. Shamir and Zoback [26] showed that the size of the slip example, we examined a fault which strikes 1151 and dips 781 and patch is on the order of the size of the anomaly of the breakout corresponds to a localised rotation in breakout position at about formation. The magnitude of Dts is a percentage of the available 131 m measured depth in the LIC118 borehole (Fig. 9A). Based on shear stress in the slip direction and controls the magnitude of the the length of the breakout rotation, we estimated a square fault anomaly. Next, the breakout formation around the faults was patch of 64 m2 centred on the borehole. Slip on a fault of this size modelled based on the combined effects of the fault-perturbed and orientation in the mining-perturbed stress field would have a

Fault Slip Resulting in Breakout Rotation Likelihood of Slip Based on CFF as a function of fracture pole orientation BottomTop Bottom BottomTop Bottom (lower hemisphere projection)

Virgin Stress State Mining-Perturbed Stress State

CFF, MPa CFF, MPa N N 130 130 Fault 0 0 -7.2 -10 -14.4 -20 135 135 -21.6 -30 -28.8 -40 Measured Depth, m -36.0 Measured Depth, m 140 140

Observed Breakouts Modeled Breakouts 145 145 Left Right Left Right Fault Slip Resulting in Gap in Breakout Occurence BottomTop Bottom BottomTop Bottom Likelihood of Slip Based on CFF 96 96 as a function of fracture pole orientation (lower hemisphere projection)

Virgin Stress State Mining-Perturbed Stress State 100 100 N CFF, MPa N CFF, MPa 0 0 -7.2 -10 104 104 -14.4 -20 Fault -21.6 -30 108 108 -28.8 -40 Measured Depth, m Measured Depth, m -36.0 -50

112 112

Left Right Left Right

Fig. 9. Two examples of modelling breakouts near critically stressed faults. (A) Modelling fault slip that resulted in a rotation in the breakout position. On the left, fault plane poles are plotted on a lower hemisphere stereonet and colour coded with CFF for both the virgin and mining-perturbed stress ﬁelds at the fault location. The analysed fault orientation is indicated by the black X. The right centre panel shows the borehole image log data and interpretation of the fault and breakouts. The data is shown as an unwrapped borehole in a reference frame of looking down the borehole. The right panel compares the observed breakouts (green) with the modelled breakouts (blue). The fault is shown in red (red). (B) Modelling slip on a fault that resulted in a gap in breakout occurrence. The panels are the same as described for A.

10 A.M. Lucier et al. / International Journal of Rock Mechanics & Mining Sciences ] (]]]]) ]]]–]]] rake of 43.31 and 6.3 mm of dislocation. Assuming a complete van Asegen and Gerhard Hofmann of ISS International for their stress drop, the stress relief would be 23.4 MPa. Based on this fault help with Map3D. Thanks to AngloGoldAshanti for the permission perturbed stress field, the predicted breakout formation closely to use the TauTona mine data for the modelling. This work is matched the observed local breakout rotation. supported by the National Science Foundation under Grant no. In Fig. 9B, we illustrate that slip on critically stressed faults 0409605 (NELSAM). Any opinions, findings, and conclusions or observed in the LIC118 borehole image log can also be associated recommendations expressed in this material are those of the with the gaps in breakout. A fault striking 1261 and dipping 531 author(s) and do not necessarily reflect the views of the National was observed at 106.4 m measured depth. The local stress Science Foundation. Other sponsors of this work include Inter- perturbation associated with slip on a 100 m2 square fault patch Continental Drilling Program (ICDP), AngloGoldAshanti, ISS Inter- of that orientation (i.e., 11.4 mm of slip with a rake of 58.91) national, and National Research Foundation (NRF). centred on the borehole with a complete stress drop (33.6 MPa) resulted in a gap in the formation of breakouts around it. This was consistent with the breakout observations at that depth, providing Appendix A further support for the far-field state of stress that was constrained in this work. Section 3.3 outlines the assumptions used to estimate the initial far-field stress state which defines the initial conditions for the BEM calculations. To constrain the range in far-field stress 5. Conclusions and recommendations states consistent with the observed data, the limits of these assumptions were systematically tested by repeating steps 3–5 of The state of stress around TauTona was determined to be in a the workflow (Fig. 4). The limits of the horizontal stress normal faulting regime with ENE and WSW dipping normal magnitudes tested were constrained by frictional failure theory. faults being critically stressed. Because the stress state is critically For a specified Sv , Pp, and m, the frictional failure limits for both stressed, stress perturbations, such as those associated with SHmax and Shmin can be defined using a ‘‘constrain stress’’ polygon the stope excavation, can reactivate faults at orientations that [31] (Fig. A1a). The ‘‘stress space’’ defined by the polygons limits were previously stable. The implications of this are currently the range of stress magnitudes that were tested for validity in this being investigated with respect to specific faults observed in analysis (Fig. A1a). the mine. Fig. A1b shows the region of the stress polygon that represents The workflow developed in this paper combines elements of a normal faulting (NF) regime. The combinations of horizontal techniques that are used to constrain stresses in deep boreholes stress magnitudes tested in this analysis are labelled numerically and oil and gas wells [12] along with boundary element modelling 1 though 8. In Fig. A1c, the stress orientations used in some of the to constrain the far-field stresses near a deep underground mine. models are labelled alphabetically A through D. We refer to the Without the BEM, the data collected in the near-field boreholes models in terms of these labels. For example, the initial stress could not be effectively interpreted, therefore, the incorporation model which has the magnitudes summarised by the blue circle of the BEM calculations of the mining-induced stress perturbation labelled (1) in Fig. A1b and the orientations of the blue symbols is an essential step in this workflow. The implementation of the labelled A in Fig. A1c is called model 1A. The assumptions that workflow in this study also indicates ways in which it could be were tested are: (1) normal faulting stress regime with vertical improved upon. Although, we recognise that there are a number and horizontal principal stresses, (2) horizontal stress orienta- of operational and financial constraints of working in an active tions, (3) Sv magnitude, (4) Pp magnitude, (5) Shmin magnitude, mine. First, one or more long boreholes that extend into the far- and (6) SHmax magnitude. field stress state must be logged with a borehole camera to assess borehole failures in the virgin stress field. Increasing the number of boreholes that reach the far-field with different borehole A.1. Stress regime trajectories will result in a more well-constrained stress model. In the near-field to the excavation, logging of vertical boreholes is The first assumption for the initial stress model was that the preferable to deviated boreholes both for the ease of data principal stresses are oriented vertically and horizontally and the acquisition and data analysis. These boreholes should be at least vertical stress is greater than the horizontal stresses. To test 10 m long (although longer boreholes are preferred) and located whether the stresses are aligned vertically and horizontally, we away from complicated tunnel intersections. The optimal loca- analysed stress models with the stress magnitude parameters of 2 tions of the boreholes should be chosen based on preliminary BEM (Fig. A1b) and with the vertical stress deviated 101,151, and 201 results. Boreholes should be located where there is minimal from vertical. First, Sv was deviated from vertical towards an complexity of the mining perturbed stress state and where the azimuth of 3451 (the azimuth of S1 from the overcoring mining-perturbed stress state is likely to result in borehole measurements). The S2 azimuth was fixed at 1551, but the S2 failures. Our final recommendation is that Pp and the S3 inclination angle and S3 orientation were adjusted as S1 was magnitude should be measured in the boreholes that reach the deviated to maintain the orthogonal nature of the principal far-field. The S3 magnitude can be measured with minifrac tests, stresses. As the deviation angle increased, the breakout positions which are commonly used in oil and gas wells. Having a modelled in the far-field of the LIC118 borehole-rotated clockwise measurement of S3 would decrease the number of assumptions around the borehole wall (looking down the borehole). The that are needed to constrain the stress state and would result in a predicted breakouts from the initial stress model were centred at more precisely constrained far-field stress state. 97–2771 from the bottom of the hole. For a stress state with Sv deviated 201 to the NNW, the breakouts were predicted at 108–2881 from the bottom. The observed breakouts are centred

Acknowledgments at approximately 105–2851. Therefore, the deviation of S1 from vertical towards the NNW resulted in a more consistent ﬁt to the This work was made possible, thanks to invaluable help by observed breakouts in the LIC118 borehole and had little to no Hannes Moller, Pieter van Zyl, and many underground workers in effect on the failures modelled in the shorter boreholes in the TauTona mine of AngloGoldAshanti. We would like to thank Gerrie near-ﬁeld of the mining.

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Fig. A1. Constraining the far-field stress state. (A) The ‘‘constrain stress’’ polygons defined by frictional faulting theory for m ¼ 0.6, 0.8, and 1. The stress regimes are labelled as NF ¼ normal faulting, SS ¼ strike-slip faulting, and RF ¼ reverse faulting. (B) Enlarged view of red box in (A). Stress magnitude parameters for models 1 through 8 that were tested are shown by circles and the acceptable range of stress magnitudes for the far-field stress model is shown by the green-shaded area. The blue circle is the initial stress model, the green circles fall within the acceptable magnitude range for the far-field stress model, and the red circles fall outside the acceptable range of stress magnitudes. (C) Lower hemisphere plot of stress orientations. The green-shaded areas are the acceptable range in orientations for the principal stresses. The blue model (A) is the initial stress model, the red model (B) is not acceptable, the black models (C) were used to test the range in horizontal stress orientations, and the green model (D) is a model with an average acceptable orientation.

We also tested the sensitivity of the modelling to the azimuth towards the NNW (Fig. A1c). Because S1 is nearly vertical, we refer of S1 by rotating the azimuth by 751 from 3451. This slight to it as Sv . rotation did not have a signiﬁcant effect on the modelled failures. The initial stress model also assumed that the stress regime

However, when S1 is deviated 201 from vertical towards an was normal faulting, as indicated in McGarr and Gay [10]. azimuth of 1651 and S2 is deviated 201 from horizontal with This assumption was tested using model 4D, a strike-slip an azimuth of 3351 (stress model 2B in Fig. A1), the breakouts faulting stress model in whichSHmax ¼ 30 MPa=km4 Sv ¼ modelled in the LIC118 borehole were positioned at 851 and 27:2 MPa=km4Shmin ¼ 14 MPa=km (Fig. A1). Because breakouts 2651 from the bottom of the hole. The conclusion from these form normal to the direction of maximum compression along the tests was that S1 is likely deviated up to 10–201 from vertical borehole, a subhorizontal S1 acting on a subhorizontal borehole

12 A.M. Lucier et al. / International Journal of Rock Mechanics & Mining Sciences ] (]]]]) ]]]–]]]

Table A1 Observed and modelled positions of DITFs and breakouts (BO) in degrees from north for 3 vertical boreholes

Borehole Image log observations SHmax Azimuth: 168 SHmax Azimuth: 155 SHmax Azimuth: 148

DITF BO DITF BO DITF BO DITF BO

Site 7V 170 162 156 150 Site 10 60 80 72 66 Site 13 152 62 167 77 160 70 154 66 results in breakouts modelled closer to the top and bottom of the range of m (0.6–1.0) for the brittle crust [22,27]. Rock mechanics borehole rather than near the sides of the borehole, as observed. experiments measured a m ¼ 0.82 for the quartzite and a m ¼ 0.58

The larger magnitude of S1 also modelled larger breakout widths for the cataclasite that is found in the fault trace of many pre- (up to 1801) than the observed widths of about 601. These results existing faults [14]. The ‘‘constrain stress’’ polygon, which is are inconsistent with the breakout observations. deﬁned by frictional faulting theory, decreases in size with

decreasing values of m [31] (Fig. A1a). For Pp ¼ 10 MPa/km, A.2. Horizontal stress orientations Sv ¼ 27:2 MPa=km, and m ¼ 1, the lower limit of Shmin is 12.9 MPa/km, while if m ¼ 0.6, Shmin is limited to 15.5 MPa/km. To test the magnitude of S , we analysed the borehole In the initial model, the azimuth of SHmax (S2) was 1551 and hmin failure modelling results based on BEM calculations using stress Shmin (S3) was 2451. Since the trajectory of Sv is likely slightly models 2D and 3D (Fig. A1). For the LIC118 borehole, both stress deviated from vertical, S2 is also likely to be inclined horizontal, models predicted breakouts consistent with the far-field observa- and is, therefore, referred to as SHmax . We tested the effects of tions. Model 2D (m ¼ 1.0) is more consistent with the near-field rotating the azimuth of SHmax clockwise to 1681 and counter- clockwise to 1481 (shown by the black open circles in model 2C in observations. The breakout widths predicted at sites 10 and 13 Fig. A1) on the borehole failure modelling. Rotating the horizontal and at the top of LIC118 more closely matched the observations. stress azimuths had very little effect on the breakouts modelled The DITFs at site 10 and 7 V were also better represented with along the LIC118 borehole. However, it had a significant effect on stress model 2D. There was no significant difference between the the orientations of the failures modelled in the near-field vertical two models in the other boreholes. While model 3D was less consistent with the near-field observations, it could not be ruled boreholes (Table A1). The SHmax azimuth of 1481 resulted in a better fit to the observed borehole failure positions at sites 10 and out. For this reason, the Shmin gradient was constrained to be 13, while an azimuth of 1681 was more consistent with site 7 V between 12.9 and 15.5 MPa/km (Figs. 8 and A1b). failures. Therefore, the range of acceptable SHmax azimuths was constrained to be between 1451 and 1681 with an inclination up to A.6. SHmax magnitude 201 from horizontal (Figs. 7 and A1c).

The initial stress model assumed that the SHmaxbShmin. To test A.3. Vertical stress magnitude this assumption, we compared the failure predictions from three

stress models: 5D, 6D, and 7D, where the SHmax gradients are 25, The Sv magnitude was well constrained based on the density 22.5, and 20 MPa/km, respectively (Fig. A1). All the stress models 3 of the overburden material which is about 2700 kg/m . Further- predicted borehole failures that were consistent with the far-field more, the breakouts in the far-field of the LIC118 borehole are breakout observations in the LIC118 borehole. In general, the primarily controlled by the magnitude Sv and the uniaxial borehole failure models based on the BEM calculations using the compressive strength of the rock. In this work, we used a uniaxial smaller SHmax gradients better represented the absence of break- compressive rock strength of 200 MPa from laboratory measure- outs that was observed at the top of the LIC118 (Fig. 6), but were ments [15] to model the breakouts. Increasing the magnitude of not as consistent with the other near-field observations. The Sv resulted in breakout widths that were too large and decreasing borehole failure modelling based on stress model 7D predicted it resulted in breakout widths that were too small. Based on this the absence of failures at the top of the LIC118 borehole and the analysis, the Sv gradient ranges from 26.7 to 27.3 MPa/km. breakouts at site 10, but does not predict any breakouts at site 13 or any DITFs at site 7 V. Because of the lack of consistency with the A.4. Pore pressure near-field borehole observations, we excluded stress model 7D from the range of acceptable far-field stress states. We constrained

The initial stress model had a hydrostatic Pp gradient of the range of SHmax gradients for a gradient of Shmin of 14 MPa/km 10 MPa/km. This assumption was consistent with the observations (m ¼ 0.8) to be 22.5–25.5 MPa/km. The acceptable SHmax range is that the crust around TauTona is critically stressed. As mentioned smaller (25–26 MPa/km) for an Shmin of 15.5 MPa/km (m ¼ 0.6) above, hydrostatic Pp is typically observed in deep boreholes in and larger (21–25) for an Shmin of 13 (m ¼ 1.0) (as shown in the low porosity (o2%) and very-low permeability crystalline base- green shaded regions of Figs. 8 and A1b). ment rocks in intraplate regions [22–24]. Without any direct measurements of Pp, we continued to assume Pp is hydrostatic for References all the analyses, and to constrain S3, as discussed in the next section. [1] Gane PG, Hales AL, Oliver HA. A seismic investigation of the Witwatersrand earth tremors. Bull Seismol Soc Am 1946;36:49–80. [2] Gane PG, Seligman P, Stephen JH. Focal depths of Witwatersrand tremors. Bull A.5. Shmin magnitude Seismol Soc Am 1952;42:239–50. [3] McGarr A, Spottiswoode SM, Gay NC. Relationship of mine tremors to induced stresses and to rock properties in the focal region. Bull Seismol Soc Am In the initial stress model, the S3 magnitude was limited by a 1975;65:981–93. coefﬁcient of sliding friction of m ¼ 1.0 in a critically stressed [4] Reches Z. Building a natural earthquake laboratory at focal depth. In: crust. This value of m is the upper limit of the generally assumed Proceedings IODP-ICDP Fault Zone Drilling Workshop. Miyazaki, Japan, 2006.

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Please cite this article as: Lucier AM, et al. Constraining the far-ﬁeld in situ stress state near a deep South African gold.... Int J Rock Mech Mining Sci (2008), doi:10.1016/j.ijrmms.2008.09.005